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Observations of the function, which might involve simulations or laboratory or field experiments, are both expensive and noisy. Our goal is to simultaneously learn the true parameter $\\theta$ while finding the optimal value of $x$. We develop an efficient implementation of a method, known as the knowledge gradient, that optimizes the value of information from each experiment. Our algorithm can handle $x$ and $\\theta$ that are multidimensional continuous vectors. We prove that our algorithm asymptotically learns the correct $\\theta$ and the best value of $x$. Experiments show that the algorithm produces fast convergence, even in higher dimensions.<\/jats:p>","DOI":"10.1137\/17m1129301","type":"journal-article","created":{"date-parts":[[2018,10,18]],"date-time":"2018-10-18T21:08:52Z","timestamp":1539896932000},"page":"2945-2974","source":"Crossref","is-referenced-by-count":1,"title":["Optimal Learning for Nonlinear Parametric Belief Models Over Multidimensional Continuous Spaces"],"prefix":"10.1137","volume":"28","author":[{"given":"Xinyu","family":"He","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yangzhou","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Warren B.","family":"Powell","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,10,18]]},"reference":[{"key":"atypb1","first-page":"39","author":"Agrawal S.","year":"2012","journal-title":"Proceedings of the JMLR Workshop and Conference on Learning Theory"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623496312848"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1023\/A:1021810301763"},{"key":"atypb4","unstructured":"J.Y. 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